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%I #1 May 11 2007 03:00:00
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,1,1,1,
%T 1,0,0,1,2,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2,3,3,3,2,2,1,1,1,2,2,
%U 1,1,1,1,1,2,2,2,1,1,1,1,0,1,2,2,2,2,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,2,2,1
%N Length of longest string of consecutive zeros in the base-7 expansion of 2^n.
%C Is a(n) >= 3 for all n >= 8834?
%e a(42)=2 because the base-7 expansion of 2^42 is 113200616214553321.
%o #!/usr/bin/perl -l $|++; use Math::GMP; use strict; my $n = new Math::GMP 1; my $pow = 0; while (1) { my $base7 = basebexpansionofn(7, $n); my $maxconsecutivezeros = 0; while ($base7 =~ /(0+)/g) { if (length($1) > $maxconsecutivezeros) { $maxconsecutivezeros = length($1); } } print "a($pow)=$maxconsecutivezeros"; $n *= 2; $pow++; } sub basebexpansionofn { my ($b, $n) = @_; return '0' if $n == 0; my $lastdigit = $n % $b; my $firstdigits = ($n - $lastdigit)/$b; return ($firstdigits ? basebexpansionofn($b, $firstdigits) : '').$lastdigit; }
%K nonn
%O 0,39
%A Josh Purinton (joshpurinton(AT)gmail.com), Apr 06 2007
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